The measurement of soil moisture and bulksoil salinity using time domain reflectometry

R.B. BONNELL, R.S. BROUGHTON and P. ENRIGHT

Department ofAgricultural Engineering, Faculty ofAgricultural and Environmental Sciences, Macdonald College ofMcGillUniversity, 21111 Lakeshore Road, Ste. Anne de Bellevue, PQ, Canada H9X ICO. Received 22 November 1990; accepted 21March 1991.

Bonnell, R.B., Broughton, R.S. and Enright, P. 1991. The measurement of soil moisture and bulk soil salinity using time domainreflectometry. Can. Agric. Eng. 33:225-229. The use of time domainreflectometry (TDR) for the measurement of soil volumetric watercontent is confirmed to be valid over a wide range of soil moisturelevels, even when the soil is moistened with a complex saline solutionsuch as may be found in any groundwater. The TDR technique offersa non-destructive, safe, instantaneous means of measuring soil moisture. It is found that the trace recorded can also be used to ascertain

absolute solution salinity levels, but only relative levels of bulk soilelectricalconductivity (ECa) are possible. More research is required todetermine the effects of the soil matrix on electrical parameters involved in TDR recordings before absolute ECavalues can be obtained.

L'usage de la reflectometrie temporelle (TDR)pour revaluation dela teneur volumique en eau des sols s'est avere valide pour une largegammedeniveauxd'humidite du sol, meme lorsque le sol est humecte(Tunesolution saline complexe, comme on en trouve dans toutes leseaux souterraine. La technique TDR offre un moyen non-destructif,sur, et instantane de mesurer Fhumidite du sol. II fut determine que latraceenregistree pouvait aussi etre utilisee pour revaluation absoluedu taux de salinite d'une solution. Mais seuls les niveaux relatifs de laconductivite electriquedes sols en vrac peuvent etre mesures. Desrecherches supplementaires sontnecessaires pourdeterminer leseffetsde la matricede sol sur les parametres electriques impliquesdans lareflectometrie temporelle afinde pouvoirobtenirdes valeurs absoluesde la conductivite electrique.

INTRODUCTION

The need for an accurate, quick, non-destructive means ofmeasuring soilmoisture (0) andbulk soilelectrical conductivity (ECa) at the sametime requires no explanation. Possibly,time domain reflectometry (TDR) offers such a means.

In recent years TDR has become an accepted means ofmeasuring soil moisture (Hayhoe et al. 1983, Patterson andSmith 1981; Stein and Kane 1983; Topp and Davis 1981; Toppand Davis 1982). It is an extremely useful method. It can beusedboth in laboratoryand field conditions, is non-destructiveandrapid, can be automated (Baker and Allmaras 1990),andit is independentof soil type, soil density and soil temperature(Toppetal. 1980).

Its use for determining ECa has not been clearly establishedand requires a better understanding of the complexities of thedielectricbehaviour of a soil matrix. The objectives of this paperareto put forth furtherdetails in an attempt to enhance the database upon which researchers can attempt to solve this dilemma; to ascertain the usefulness of the procedures suggestedby Daltonand van Genuchten (1986); and to measure ©tdr ofsoils moistened with naturally occurring groundwater.

CANADIAN AGRICULTURAL ENGINEERING

Time Domain Reflectometry is a technique involving a highfrequency electric pulse which, in soils applications, measuresthe dielectric constant (electrical permittivity) of the soil matrix. A transverse electromagnetic wave (TEM) is propagatedalong conducting probes inserted into the soil. At the frequencies used, water has a dielectric constant of 80 as compared tovalues of 2 to 5 for soil solids and 1 for air. Thus, a measure ofthe dielectric constant of a soil can be related to its water

content. This was first explored by Fellner-Feldegg (1969) forfluids, and has been developed for soils by Topp et al. (1980).Also, it has been noted that the degree of attenuation of theelectric pulse in the soil has some relationship to the bulkelectrical conductivity of the soil, but this relationship has notbeen fully established (Yanuka et al. 1988).

THEORY

When a TEM is guided along metal probeswhich areinsertedin soil, the soil matrix serves as the dielectric medium. Thesignal is reflected from theendsof the probes backto theTDRreceiver. The form of the wave can be displayed on an oscilloscope.

Figure 1 illustrates an idealised wave form. Point A is thepointwhere the probe enters the soil. The outputof the TDRtransmitter on the oscilloscope is the reflection coefficient ofthe probe-soil circuit asa function of distance (orsignal traveltime) relative to theTDR unit.This reflectioncoefficient(r) isthe ratio of the voltage reflected back to the receiverdividedby the voltage applied by the TDR unit. When the emittedpulseenters the probe-soilrealm, nearlyall of the electromagneticenergycomes back through the "ground" so r approaches-1, and the curve drops. Conversely, at the open end of theprobes (pointC) nearlyall of the energy is reflectedback andr approaches 1. Some energy losses are incurred along thecable lengths and connections so r never reaches 1 or -1 butvaries between these extreme values. The distance (x) frompoints A to pointC is proportional to the dielectric constant ofthe soil and in turn to 6.

The second parameter that can be measured from the traceis the ratio of the reflected to the incident wave; given byVr:Vt (Fig. 1). This ratio is used to determine ECa. Themagnitude of the reflected wave will decrease as the soilsalinity increases, due to increasing attenuation of the propagating wave front.

225

DISTANCE

Fig. 1. Stylized TDR trace. At point A, the wavefrontenters the soil and at C it reaches the probe theends, x represents distance from A toC as seen byTDR unit. VT is ratio of transmitted to reflectedwave along probes and VR is the same ratio at theend of probes.

Determining soil water content

The dielectric constant, AT, is related to signal propagationvelocity, v,by (Wobschall 1978; Selig andMansukhani 1975;Topp and Davis 1985):

v = c/Km (1)

where c =propagation velocity ofanelectromagnetic wave infree space (3 x 10 m/s).

In practice, the velocity is determined from knowing thelength of the probe, L, in the soil and measuring the signaltravel time, t. The horizontal scale of the oscilloscope used(Tektronix 1502B) gives readings in terms of distance travelled as seen by the scope. By relating this scope distance, x,to theknown probe length, actual time of travel is obtained.Thus,

t=x/c (2)

andcombining Eqs. 1 and 2 gives:

K=(c/v)2 = (x/L)2 (3)

The relationship betweenK and the volumetric watercontent was determined empirically byTopp etal.(1980) and hassince been substantiated by numerous authors (Malicki andSkierucha 1987; Simpson and Meyer 1987; Dalton etal. 1984;Davis and Annan 1977). The empirical equation used todetermine volumetric moisture content is:

0 =(-5.3*10"2M2.9*10"2^)-(5.5*10"4^2)+(4.3*10-V) (4)

Topp et al. (1984) have shown that, under field conditions,the TDR measurements of soil water content were within2%of those measured gravimetrically. Also, Keng and Topp

226

(1983) have shown that both gamma-ray attenuation and TDRmethods measured soil moisture to the same degree of accuracy, as compared to the standard gravimetric method.

Determination of soil bulk electrical conductivity

According to electromagnetic field theory (Ramo and Whinn-ery 1959), if the imaginary component of the dielectricconstant is negligible, the amplitude of a perfectly reflectedsignal travelling along an electric medium with an attenuationcoefficient of a is given by:

V/? = VYexp(-2oL) (5)

For soils low in magnetic materials, the attenuation coefficient is given by (Daltonand van Genuchten 1986):

a = 6QnECa/Km

CombiningEqs. 5 and 6 yields:

ECa =(Km/120nL) ln(VT/VR)

(6)

(7)

The relationship between an increase in electromagneticwave front attenuation corresponding to an increase in soilsalinity hasbeennotedandexplored by a number of researchers (Dalton et al. 1984; Dasberg andDalton 1985; Dalton andvan Genuchten 1986; Zegelin etal. 1989, Topp etal. 1988; vanLoon et al. 1990). In practice, determining the TDR signalattenuation is very complex, becausewe need to measure allreflections between the TDR source and the reflection ofinterest (reflections occur at all connections and line typechanges).

MATERIALS AND METHODS

Initially, measurements were performed on water solutions ofvarying salinity levels. Solution concentrations ranged from0.2 to 8.5 dS/m. These solutions were placed in PVC cylinders,measuring 200 mm in diameter and 200 mm in length. Thesolution conductivity was first measured using a standardconductivity meter. The 4-probe wenner array approach asoutlined byRhoades and Halvorsin (1977) was used; with theexception that the probes were not concentrically positioned,butspaced 30mm apartina straight lineandinserted horizontally through holes drilled inthe sideofthe cylinders. With thismethod, it is recommended that probe insertion length belimited to amaximum of"probe spacing divided by 20" (in thiscase only 1.5 mm). This is to maximize conductance in theambient and notthe probes themselves. (For interest, becausethe TDR method utilizes longer probes (in this experimentL=82.6 mm), wenner array values were also recorded usingprobe lengths identical tothe TDR rod lengths.) Finally aTDRtracewasrecorded andanalyzed as outlinedby Dalton andvanGenuchten (1986)usingEq. 7.

Four probes are required for the wenner array, while onlythe two inner probes were used for the TDR method. In thiswayalmosttheidenticalsampleis usedfor bothmeasurementsofelectrical conductivity. The 4-probe (EC4P) readings wereperformed using a Meggar ET3 Earth Tester. The TDR data(ECtdr) wererecordedusing a Tektronix 1502B cable tester

BONNELL, BROUGHTON and ENRIGHT

connected via a 50 ohm coaxial cable to a TP-103 impedancematching transformer, or balun, in turn connected to a parallelTV cable attached to the steel probes. Similar measurementswere then performed on soils.

Five replicate samples of a sandy loam (10% clay, 70%sand, air dried and passed through a 2 mm sieve) were packed(mean bulk density of 1.7 Mg/m ) into 200 mm diameter PVCcylinders, 200 mm in length. Waters of various salt contents(0.2 to 8.5 dS/m) were introduced into the soil samples via anentrance hole in the base of the PVC cylinders. Various saltconcentrations were obtained by diluting, with distilled water,samples taken from well water having a total dissolved saltcontent of 12 g/1. To date, researchers have only utilizedsimple saline solutions, fabricated in the laboratory (Topp etal. 1980; Dalton and van Genuchten 1986; Yanuka et al. 1988).The question arises as to whether the inherent chemical complexities of a naturally occurring groundwater will alter theresults. A small positive head was maintained and the sampleswere allowed to saturate by capillary rise over a period of fourto eight days. Both ECtdr and EC4P readings were taken byinserting 1.5 mm diameter stainless steel probes into the soil82.6 mm, spaced at 30 mm.

Core samples (50 mm diameter by 50 mm in length) werethen taken to determine soil water content, gravimetrically.Finally, water extracts wereobtained when possible, by insertinga ceramic tip intothesoilbetween theprobesandapplyinga suction.These extracts were analyzed for salt content (ECW).

RESULTS and DISCUSSIONS

Thedatapointsdepictedin Fig. 2 were obtainedover a rangeof soil ECa levels from 0.2 to 8.5 dS/m. This clearly illustratesthe independence of ©tdr from soil salinity. The use of anatural saline water did not alter this independence, alreadycorroborated bysuch authors asTopp et al. (1988) andZegelinet al. (1989). Correlation of soil moisture determinations bygravimetric and TDR means were found tohave anR-squaredvalue of 0.91.

TDR VS GRAVIMETRICSOIL MOISTURE MEASUREMENT

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Fig 2. Comparison of measured volumetric soil moistureusing TDR and gravimetric methods. Thesereadings were taken at ECa values ranging from0.2 to 8.5 dS/m.

CANADIAN AGRICULTURAL ENGINEERING

Electrical conductivities of aqueous solutions were measured by three means; a conductivity probe, the 4-probewenner array and the TDR. Conductivity values obtained withthe TDR and the 4-probe wenner array were essentially equalto those obtained with a conductivity probe (Fig. 3). The valueof R-squared was 0.99 and 0.97 for 4-probe and TDR respectively. The TDR method is less sensitive at higher salinitylevels because the high degree of attenuation causes the reflected signal to be so small that it is difficult to measureaccurately. Also, it is difficult to accurately determine rodlength in the soil. Surface features of the soil can easily account for an error in measurement of one or two millimetres.

An actual rod depth of 83 mm measured as 82 mm will alterthe resultant ECtdr by 2.5%.

It is interesting to note that the 4-probe wenner array valueson the graph were obtained from determinations using bothshort (1.5 mm) and long (82.6 mm) rods. It was found that theEC4P values obtained using the long rods were two times thevalues obtained using the short rods.

EC CALIBRATIONSSaline Solutions

E

a:

Q.

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Fig 3.

Water Electrical Conductivity dS/m• 4-probe + TDR

Comparison of measured solution salinity usingTDR and 4-probe null balancemethods againstastandard conductivity probe.

The excellent agreement betweenECtdr and EC4P holdstrue only for saline solutions (Fig. 3). The correlation is notvalid when measuring saline soils (Fig. 4). Although it isimportant to note that the TDR values are generally of thesameorderof magnitude andthat thevaluesroseandfell in theexpected pattern (as more saline solutions were introducedinto the soil, the degreeof signal attenuation did increase) thecorrelation with the 4-probe values was extremely poor (R-squared 0.50). Values of Vt andVr are measured at differenttime positions, andaccording to Toppet al. (1988) areerroneousbecause thedegreeof attenuation is a function ofplaceandtime of measurement. Indeed Eq. 7 has been found to beinvalid for the saline soils used in this study.

However, some relationship between ECa and degree ofattenuation is evident. It was noted in the laboratory that TDRtraces for soils of low salinity would appear as line 'A* in Fig.

227

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Fig4. Comparison of soil salinity measured by 4-probeand TDR methods over a range of soil moisturelevels (air dry to 0.34).

salinity)

time

Fig 5 a). Changes in a TDR trace as EC increasesfrom a high 'A' reflection value to a low 'B'value. The smallerxb corresponds to a lowermoisture level in the soil asevaporation progresses.

Reduction of VTas ECw increases

2 4 6 8 10 12 14 16

Soil Extract Conductivity dS/m+sandy loamsand

Fig5 b). Illustration of howheightof signal reflection atthe end of the probes, Vt, decreases as ECWincreases.

228

5a, evident of a high reflection at the ends of the probes. Thenas evaporation from the cores occurred, the salt concentrationof the soil water would increase and the TDR trace would

progressively approach a trace similar to that of line 'B\ Fig.5b illustrates how values of Vt relate to final soil solution ECWlevels recorded. Again, a general pattern of lower Vt valueswith higher ECW values is evident.

Topp et al. (1988) suggest Eq. 7 is not valid because theimaginary part of the dielectric constant was not found to benegligible by them, but is a factor of nonuniform impedancemismatches which occur at all cable junctions. A new approachby vanLoon et al. (1990)corrects for all the impedancemismatches by usinga referencepoint (x0) on theoutputgraph(with the probes in air). Based on the assumption that anyattenuationdue to the measuring device itself is a constant andby superpositionof a base (V0), Eq. 7 becomes;

4/2ECa = (Kl'V120nL) ln(V0/V0R) (8)

where VoR is measured, with the probes in the soil, at the same"time" position as was the reference V0. This is not the case forVt and Vr in Eq. 7 which are measured at different timepositions. The differencein magnitude between Vo and VoR isrepresentative ofthe change in the environment being measured.That is,air for V* and thesaline soil-matrix for VoR. Thus, oneavoids theproblems of measuring reflectance at different timesand inessence, calibrates any one particular instrument configuration. Once the calibration figure is known the only requireddata is Vqr to solve forECa. Theapproach of vanLoon et al.(1990)was not known at the time of measurement.

CONCLUSIONS

It has been substantiated that volumetric soil moisture determinations via TDR techniques are valid and accurate, evenwhen the soil contains acomplex saline solution such as maybe found in natural groundwater.

Insertion of the TDR dual probes at points along a soilprofile will yield oscilloscope traces which can be used tomonitor relative changes insoil salinity (Fig. 5b). But determination ofabsolute ECa values were found tobeincorrect whenEq. 7 was used. Equation 7, which isbased upon the assumption that the imaginary portion of the dielectric constant isnegligible, isvalid for measuring aqueous salinity levels. However, thisassumption has been shownto be invalidfor soils.

The use oflonger than recommended probe lengths (amaximum of 20 percent of rod spacing is recommended byRhoades and Halvorson 1977) is possible when using thefour-probe wenner array for ECa, if a linearcalibration factoris taken into account. This is helpful in the laboratory wherethe small size of the soil samples analyzed would otherwisenecessitate quite short probes. With very short probes, it isdifficult to assure good probe-soil contact. In this study, alengthto spacingratio of 2.75:1 rather than the recommended1:20 was used, and a correction factor of 2.0 was found to beappropriate.

Currently a laboratory investigation is being performed, todetermine any dependence ofECtdr upon clay content and/orthe chosen number of reflections at which to measure thereflection coefficients (thex0value of vanLoon et al. 1990) ofEq. 8.

BONNELL, BROUGHTON and ENRIGHT

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial support forthis research from: The Brace Research Institute of McGillUniversity; Natural Sciences and Engineering Research Council of Canada; staff of the Land Resource Research Centre,Agriculture Canada; and the Canadian International Development Agency.

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